B. Whalica's Permutation Construction
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Whalica has a mysterious permutation$$$^{\text{∗}}$$$ $$$p$$$ of length $$$n$$$. Let $$$$$$ S_k = \sum_{i = 1}^{k} p_i $$$$$$ If for all $$$1 \le i \le n$$$, $$$S_i$$$ is divisible by $$$p_i$$$, then the permutation $$$p$$$ is called a good permutation.

Checking whether a permutation is a good permutation is far too easy, and Whalica would never enjoy doing something that simple. Therefore, Whalica has specially prepared another problem for you:

Given a positive integer $$$n$$$, you need to construct a permutation $$$p$$$ of length $$$n$$$ such that it is a good permutation. You need to determine whether such a permutation exists. Moreover, if such a permutation exists, output any one permutation that satisfies the condition.

$$$^{\text{∗}}$$$A permutation of length $$$n$$$ is an array consisting of $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ in arbitrary order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation ($$$2$$$ appears twice in the array), and $$$[1,3,4]$$$ is also not a permutation ($$$n=3$$$ but there is $$$4$$$ in the array).

Input

The first line contains an integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

Each of the next $$$t$$$ lines contains an integer $$$n$$$ ($$$1 \le n \le 5 \times 10^5$$$) — the length of the permutation you need to construct.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^6$$$.

Output

For each test case, the first line contains a string indicating whether such a permutation can be constructed. If it is possible, output $$$\mathtt{YES}$$$; otherwise, output $$$\mathtt{NO}$$$.

If such a permutation can be constructed, output any one permutation that satisfies the conditions on the second line.

Note that the output is case-sensitive.

Example
Input
3
1
3
4
Output
YES
1
YES
2 1 3
YES
3 1 4 2